Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy

Abstract

We investigate the effect of linear independence in the strategies of congestion games on the convergence time of best response dynamics and on the pure Price of Anarchy. In particular, we consider symmetric congestion games on extension-parallel networks, an interesting class of networks with linearly independent paths, and establish two remarkable properties previously known only for parallel-link games. More precisely, we show that for arbitrary non-negative and non-decreasing latency functions, any best improvement sequence converges to a pure Nash equilibrium in at most n steps, and that for latency functions in class $\mathcal{D}$, the pure Price of Anarchy is at most $\rho(\mathcal{D})$.